Circular arc solar concentrator

ABSTRACT

A solar energy concentrator and collector having a concentrator made up of one or more anticlastic panels that feature a non-developable doubly curved surface. The panels are concave in the north-south direction and convex in the east-west direction. In one embodiment, the panels are formed to have parallel circular arcs in the north-south direction of increasing radius from the center of the panel to its edges and having a curved cross-section in the east-west direction. The concentrator reflects light to a narrow zone of concentration which moves within a plane in response to changes in the angle of incidence of sunlight thereon. A method for forming the specially shaped reflective fiber reinforced plastic panel is also disclosed.

This application is a division of my U.S. patent application, Ser. No.486,314, filed Apr. 19, 1983, now U.S. Pat. No. 4,538,886.

TECHNICAL FIELD

The present invention relates to a solar energy concentrator andcollecting device formed as part of a building. More particularly, thepresent invention relates to one or more anticlastic concentrator panelsadapted to reflect sunlight into a zone of concentration to be absorbedby a collector mounted to move with changes in the location of the zoneof concentration.

BACKGROUND

Various solar energy collecting apparatus are known which use areflector for concentrating solar energy at a point or in a region whereit can be absorbed by a collector for conversion into useful energy.

The primary problem facing such devices is to efficiently collect energyduring daylight hours as the sun moves across the sky. Adding to theproblems associated with daily movement of the sun is the fact that thecourse of the sun's movement across the sky is effected by seasonalchanges.

Various methods of tracking the movement of the sun across the sky havebeen developed for solar energy collectors. In some devices,particularly those with a parabolic cone shaped concentrator, such asthat shown in U.S. Pat. No. 670,916 to Eneas, the concentrator andenergy collecting device both move to follow the path of the sun'smovement. Such devices require elaborate and expensive tracking systemswhich make them impractical for collecting energy.

In another type of solar energy concentrating device, a stationaryconcentrator and collector are provided which may form a roof structure.As shown in U.S. Pat. No. 4,291,679 to Kersavage, a hyperbolicparaboloid concentrator forms the southern portion of a roof and focuseslight on a curved absorber. To compensate for seasonal changes in thecourse of the sun's movement, the Kersavage patent shows the use of twodifferently oriented reflectors. The expensive, custom designed roofstructure disclosed in Kersavage does not lend itself to widespread useof the solar energy concentrating device disclosed therein.

If a straight absorber is used with a hyperbolic paraboloidconcentrator, as shown in U.S. Pat. No. 4,035,064 to Cowman, the desiredconcentration of light occurs only along portions of the absorber withmuch of the reflected light being diffused prior to reaching theabsorber. While the Cowman device eliminates problems associated withmoving either the concentrator or the collector, the quantity of energyabsorbed per unit of concentrator surface, or efficiency of thecollector, is significantly less. Also, the quantity of light reflectedby the concentrator during the early morning and late afternoon is verylimited because only a small corner of the reflector is directed towardthe sun at those times.

In U.S. Pat. No. 4,111,360 to Barr a solar energy concentrating andcollecting arrangement is provided by forming a concave cylindricalconcentrator as part of the roof of a building and pivotably supportinga collector above the roof. The collector is movable in response tochanges in the location of the focus zone of the concentrator caused bychanges in the angle of incidence of sunlight on the concentrator. Oneproblem with this cylindrical concentrator is that the daily time periodfor efficient energy collection is severely limited since a significantportion of morning and afternoon light is reflected from theconcentrator to a location east or west of the collector.

Another problem with the structure disclosed in Barr is that the surfacedoes not have the membrane strength realized by a hyperbolic orotherwise non-developable surface. Thus a specially constructed andreinforced roof structure is required to support the concentratorsurface and maintain its shape.

Other cylindrical concentrators with movable collector systems such asthat disclosed in U.S. Pat. No. 3,868,823 to Russell, Jr. minimize thisloss of light by extending the length of the solar collector. However,due to size limitations such a solution is not feasible if the solarconcentration is to be incorporated into a building.

Therefore, prior art devices fail to provide a highly efficient yeteconomical solar collector wherein a concentrating surface is formed aspart of a building to reflect light into a narrow zone of concentration.Due to the daily and seasonal changes in the angle of incidence ofsunlight it is important that the collector moves with the zone ofconcentration. It is preferred that the zone of concentration is alinear area so that a straight collector may be used to absorb thereflected sunlight since it is easier to support and move a straightmember than a more complex shape.

It is therefore an object of the present invention to provide anefficient solar energy collector device utilizing a concentratingsurface that creates a simply shaped zone of concentration. The zone ofconcentration follows a predictable path of movement so that movement ofthe collecting device is significantly simplified.

It is an object of the present invention to provide a concentratorsurface that is effective for a long time period each day. Theconcentration of light is to be received evenly along the length of theabsorber so as not to cause hot and cold spots on the absorber.

It is also an object of the present invention to provide a strong andinexpensive roof structure that does not require a special support frameto maintain its shape and desired optical qualities.

Another object of the present invention is to provide a roof structuremade up of inexpensive modular panels that feature a non-developablesurface which must maintain the complex shape required to optimize theoptical qualities of the surface. To successfully function as a roof,the concentrator roof panels must include adequate draining means topermit precipitation to be carried away without interfering with theconcentration of sunlight.

SUMMARY OF THE INVENTION

In accordance with the present invention, a building roof incorporatinga solar energy concentrating surface having a special contour which ismade up of discrete panels is disclosed which efficiently concentratessolar energy for collection by a collector or absorber.

The contour of the concentrator surface is a concave surface in thedirection parallel to the north-south axis. The concave surface ischaracterized by a series of circular arcs of increasing radius from thecenter or crown of the panel to its lateral edge or edges.

The concentrating surface is convex in the direction parallel to theeast-west axis so that both early morning and late afternoon sunlightmay be concentrated by the surface without substantially compromisingthe efficiency of the concentrator during the peak sunlight hours of theday. The curvature of the surface in the east-west direction is a curvedarc which disperses reflected light along the east-west axis to moreevenly distribute the reflected light along the length of the collector.This is particularly true when a plurality of panels are liked togetherside-by-side so that the light reflected from adjacent panels is blendedtogether. It is to be understood that the curvature may be circular,eliptical, paraboloidal or an irregular convex surface.

The solar concentrator of the present invention is well suited for useas a building component both because of its modular construction and thestrong, unique shape of the solar concentrator. The solar concentratoris a non-developed surface which is one that can not be made from a flatsurface and will not return to a flat surface without destruction of themember. As is well-known with hyperbolic paraboloid surfaces,non-developable surfaces are highly resistant to tension or compressiveloads.

The modular construction of the present invention lends itself to use asa building component because several of the panels may be joinedtogether to form a roof of the desired size. The panels may be arrangedin east-west or north-south extending rows by joining them together onadjacent edges. According to a preferred embodiment, each panel isformed by two identical sections assembled together at the crown, orpoint of minimum concave radius in the north-south direction, with eachsection extending away from the crown to a lateral edge of maximumconcave radius in the north-south direction. Several panels may beassembled together with adjacent panels to completely fill the availablespace on the roof. Troughs formed between adjacent panels act aschannels for draining precipitation from the surface of theconcentrator.

The zone of concentration of the concentrator surface is a narrow planarzone which moves in a single plane as the angle of incidence of sunlightchanges during the day and seasonally. The simple shape of the zone ofconcentration lends itself to the use of a straight collector member forabsorbing the reflected light. The predictability of the change in thelocation of the zone of concentration permits a controlled linear motiontracking movement of the collector within a plane according to changesin the angle of incidence of sunlight during the seasons of the year andtime of the day.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view of the solar concentrator and collector ofthe present invention featuring a set of six panels secured together toform the roof structure of a building and having a cylindrical collectormovably disposed on cantilevered arms over three of the panels to followthe zone of concentration of light reflected from the concentratorsurface.

FIG. 2 is a diagrammatic view of two adjacent panels having orthogonallines to illustrate the convex/concave shape of the panels.

FIG. 3 is a diagrammatic view showing two north-south cross-sections ofa panel with ray tracings of light reflected from the two spaced concavecircular arcs as would be expected at a season of the year other than anequinox period.

FIG. 4 is a diagrammatic view showing two north-south cross-sections ofa panel with ray tracings of light reflected from two spaced circulararcs with sunlight being received from a direction normal to the surfaceat the median of the arc as would be expected around an equinox period.

FIG. 5 is a diagrammatic representation of a series of panels shown ineast-west cross-section with ray tracings of light being received at anacute angle as would occur during the morning or late afternoon.

FIG. 6 is a diagrammatic representation of a series of panels shown ineast-west cross-section with ray tracings of light being received fromdirectly above the panels as would occur at noon.

FIG. 7 is a diagrammatic three dimensional view of a panel.

FIG. 8 is a plan view of the present invention as shown in FIG. 1.

FIG. 9 is an end elevational view of the present invention taken alongline 9--9 in FIG. 8.

FIG. 10 is a front elevational view of the present invention taken alongline 10--10 in FIG. 8.

FIG. 11 is an exploded perspective view of a panel and the continguousportion of a second panel showing the connectors between adjacentsections.

FIG. 12 is a cross-sectional view taken along the line 12--12 in FIG. 8.

FIG. 13 is a cross-sectional view of the connector provided betweenadjacent base edges of two panels.

FIG. 14 is a cross-sectional view of the connector provided at theterminal edge of a single panel taken along the line 14--14 in FIG. 8.

FIG. 15 is a cross-sectional view of the connector provided at the jointbetween lateral sides of two adjacent panels taken along the line 15--15in FIG. 8.

FIG. 16 is a fragmentary view of a worm gear drive that may be providedto controllably move the collector relative to the cencentrator surfacein response to changes in the location of the zone of concentrationcaused by changes in the angle of incidence of sunlight thereon.

FIG. 17 is a fragmentary cross-sectional view of a panel surface to showthe layered construction of the same.

DETAILED DESCRIPTION

Referring now to the drawings and particularly FIG. 1, a roof 10constructed from a plurality of circular arc concentrator panels 11assembled together is shown. The circular arc concentrator panels 11have a reflector surface 12 which is anticlastic in shape and ischaracterized by a concave circular arc curvature in one direction and aconvex curved arc curvature in a second direction perpendicular to thefirst direction.

The panels 11 are retained by a frame 14 at the optimum angle forcollecting sunlight at the latitude of the roof 10. A collector 16 ismovably mounted on a cantilevered riser support 17 for movement relativeto the reflector surface 12. The collector 16 must be movable to followthe change in location of the zone of concentration, which is showndiagrammatically in FIG. 2 and indicated by the reference numeral 13,the change in location being caused by changes in the angle of incidenceof sunlight on the reflector surface 12. The riser support 17 acts as atrack to guide the movement of the collector 16.

Referring to FIG. 2, the concentration zone 13 is shown diagrammaticallyto be a narrow planar band. The panels have a north-south axis N-S and aperpendicularly extending east-west axis E-W. As shown in FIGS. 3 and 4,the panel 11 is concave parallel to the north-south axis of the panel toconcentrate light reflected therefrom to the zone of concentration. Asshown in FIGS. 5 and 6, the panels 11 are convex in the east-westdirection to reflect light impinging thereon toward the zone ofconcentration.

The surface of each panel 11 is a non-developable surface, which isdefined herein to mean a surface that may not be formed from a planarmember but instead must be generated as a curved surface. This factor isimportant because it gives the surface exceptional structural strength.The orthogonal lines shown in FIG. 2 illustrate a preferred embodimentof the invention wherein the east-west extending orthogonal lines showthat the panel features a convex shape. Conversely, the north-southextending orthogonal lines are concave circular arcs of increasingradial extent from both sides of the crown 24 or center of the panel.

Movement of the zone of concentration 13 relative to the reflectorsurface 12 in response to seasonal and daily changes in the angle ofincidence of sunlight is best shown in FIGS. 3 and 4. FIGS. 3 and 4 showtwo spaced circular arcs in the north-south direction at differentseasons of the year. FIG. 3, for instance, shows the ray tracing typicalfor a winter day while FIG. 4 shows the ray tracing typical for thevernal or autumnal equinox wherein the concentrator is positioned sothat light from the sun is received from a direction perpendicular to atangent line at the mid-point of the reflector surface 12. The twospaced north-south circular arcs are shown to illustrate that theconcentration due to the north-south curvature occurs in a similarmanner at different points on the panel 11 because the north-southcircular arcs of the panels have a common central axis "X", as will bedescribed subsequently with reference to FIG. 7.

The reflection of sunlight in the east-west direction from the surfaceof a series of panels 11 assembled together to be adjacent in theeast-west direction is shown in FIGS. 5 and 6. As the sun moves acrossthe sky from east to west the angle of incidence relative to the generalplane of the reflector surface 12 is acute in the morning, as shown inFIG. 5, then changes to perpendicular at mid-day, as shown in FIG. 6,and then becomes acute again in the late afternoon. The graphicalrepresentations of FIGS. 5 and 6 demonstrate the importance andeffectiveness of the convex east-west curvature of the surface inreflecting light toward the collector 16, as shown in FIG. 1. If thesurface were a normal cylindrical surface with its cylindrical axisextending in the east-west direction a considerable amount of light inthe morning or late afternoon would be reflected to a point west or eastof the collector respectively.

Referring now to FIG. 7, a diagrammatic three dimensional view of apanel 11 is shown to more clearly illustrate the double curvature of thepanel 11.

The concave curvature is shown by means of the crown arc Xc, the edgearc Xe, and a mediate arc Xm. The radius of arcs Xc, Xm, and Xe, fromthe central axis X, are shown as Rxc, Rxm, and Rxe, respectively. Theradius of Rxc is less than Rxm which is less than Rxe. To form a panelwhich is rectangular in the plan view the arcs Xc, Xm, and Xe must beprogressively longer as they become further removed along the Y axisfrom Xc.

The convex curvature is shown by means of several arcs Y which areidentical in size and shape. If the convex curvature is a circular arc,the radius of the arcs Y is always Ry as measured from arc Yc. Arc Yc isin the same plane as arc Xc and is spaced from axis X a distance ofr_(y) plus Rxc.

If the surface is that of a preferred form wherein the concavenorth-south curvature is a circular arc and the convex east-westcurvature is a circular arc, the shape of the surface can be betterdefined by the following equations:

1. The radius of an arc X at a given distance Y from Xc is calculated asfollows: ##EQU1##

For example:

If:

r_(xc) =20 '

r_(y) =18.5'

Y=6' ##EQU2## r_(x) =21'

2. The three dimensional change in the surface from the center of thepanel (origin of X, Y, Z in FIG. 7) is calculated as follows:

Applying the Pythagorean Theorum: r_(x) =√X² +Z² and combining withequation 1 above: ##EQU3##

The rise Z is calculated for a given point X, Y by factoring the aboveequation to the following: ##EQU4##

For example:

If:

r_(xc) =20'

r_(y) =18.5'

Y=6'

X=0 ##EQU5## Z=-1'

The reverse curve r_(y) may be any function of Y (f(y)). The generalequation in cylindrical coordinates for the reflector is:

    r=r.sub.xc +f(y)

The general equation for the reflector in Cartesian coordinates is:##EQU6## where r_(xc) is the radius of the circular arc along the crownof the reflector.

The importance of the unique shape defined by the above equations isthat sunlight is reflected from the surface to a narrow linear zone ofconcentration 13. The energy from concentrated sunlight may then beconverted to heat by a collector located in the zone of concentration.The zone of concentration will move in response to changes in the angleof incidence of sunlight on the panel 11 caused by both the dailymovement of the sun across the sky and seasonal change in the trackingof the sun.

The ability to predict the precise location of the zone of concentrationis an important feature of the present invention. In addition, it isanother feature of the unique surface of the panel 11 that the zone ofconcentration 13 moves in a plane "M" as shown in phantom lines in FIG.7. Plane "M" extends in the X and Y axis parallel to the chord X. ChordX is the line extending from opposite ends of the arc Xc.

3. A system of equations, or algorithm, for predicting the location ofthe zone of concentration is as follows:

If:

L=Latitude

Latitude in Radians is: L_(R) =L×π/180

T=Tilt of Reflector

Tilt in Radians is: T_(R) =T×π/180

D=Day of Year

H=Time of Day

The declination, or C, for day of the year D, is:

    C=0.410152×SIN (2×π/365)×(D-81)

The angle of the sun from its noon position, or H, is:

    H.sub.1 =(12-H)×2π/24

The sine of the sun's altitude angle, or SA, is:

    SA=SIN (L)×SIN (C)+COS (L)×COS (C)×COS (H.sub.1)

The cosine of the sun's altitude angle, or CA, is: ##EQU7## The sine ofthe sun's Azimuth angle, or SZ, is: If: H₁ <0.0001; then SZ=0

If: H₁ ≧0.0001; then: SZ=Cos (C)×Sin H₁ /CA

The cosine of the sun's Azimuth angle, or CZ, is: ##EQU8## Thecomponents of a vector pointing toward the sun are W1, W2, W3.

    W1=CZ×CA

    W2=SZ×CA

    W3=SA

Correcting the vector components to compensate for the tilt of theconcentrator:

    X1.sub.c =W1×Cos (T)-W3×Sin (T)

    W3.sub.c =W1×Sin (T)+W3+Cos (T) ##EQU9## Based upon the corrected vector components the location of the collector is determined from a curve fit of simulated path based upon the computer program shown subsequently.

The desired collector position, or P, is then found by:

If: |W1_(tilt) |<0.0001

Then: Alt=π/2

If: |W1_(tilt) |≧0.0001

Then: Alt=Arctan (W3_(tilt) /W1_(tilt))

If: 1.5708-|Alt|0.1745

Then: P=-11.8693×(1.5708-|Alt|)

If: 1.5708-|Alt|≧0.3491

Then: P=-10.1942×(1.5708-|Alt|)-0.2923

If: Alt<0

Then: P=-P

The position value, P, can then be used to control the collector drivesystem by well-known analog or digital circuitry.

The computer program for determining the position of the collector is asfollows:

    ______________________________________                                        10   'ALGORITHM FOR LOCATING COLLECTOR                                        20   INPUT "LATITUDE"; L                                                      30   INPUT "REFLECTOR TILT"; T                                                40   INPUT "DAY OF THE YEAR 0 TO 365"; D                                      50   INPUT "TIME OF THE DAY, 0 to 24"; H                                      55   '                                                                        60   'STEPS 70 to 90 convert degrees to radians.                              70   CONV=3.l4l593/180 'CONV is the conversion factor.                        80   L=L*CONV 'Converts latitude to radians.                                  90   T=T*CONV 'Converts tilt to radians.                                      95   '                                                                        100  C=.410152*SIN((2*3.141593/365) * (D-81) 'Computes                             declination for the day of the year D.                                   110  H=(12-H) *2*3.141593/24 'Converts time of the day to an                       angle measured from noon.                                                120  SA=SIN(L)*SIN(C) + COS(L)*COS(C)*COS(H) 'SA is                                the sin of the sun's altitude angle.                                     130  CA=(1-SA*SA) .5 'CA is the cosine of                                          the sun's altitude angle.                                                140  IF ABS(H) < .0001 THEN SZ=0                                                   ELSE SZ=COS(C)*SIN(H)/CA 'SZ                                                  is the sin of the sun's azimuth angle.                                   150  CZ=(1-SZ*SZ) .5 'CZ is the cosine of                                          the sun's azimuth angle.                                                 155  '                                                                        160  'W1, W2 and W3 are the components of a vector that points                     directly at the sun.                                                     170  W1=CZ*CA                                                                 180  W2=SZ*CA                                                                 190  W3=SA                                                                    200  '                                                                        210  'The next four lines correct for the tilt of the reflector.              220  W1TEMP=W1*COS(T)-W3*SIN(T)                                               230  W3TEMP=W1*SIN(T)+W3*COS(T)                                               240  W1=W1TEMP/(W1TEMP 2+W3TEMP 2) .5                                         250  W3=W3TEMP/(W1TEMP 2+W3TEMP 2) .5                                         255  '                                                                        260  'Based on the corrected sun vector, the remaining lines                       locate the collector. The location is from a curve fit to data                generated with computer simulations of the Pulsar solar                       system.                                                                  270  IF ABS(W1)<.0001 THEN ALT+3.141593/2                                          ELSE ALT=ATN(W3/W1)                                                           'ALT is the altitude of the sun relative to                                   the tilted reflector.                                                    280  IF 1.5708-ABS(ALT)<.1745                                                      THEN POSTION=-11.8693*(1.5708-                                                ABS(ALT)):GOTO 310                                                       290  IF 1.5708-ABS(ALT)<.3491                                                      THEN POSITION=-10.1942*(1.5708-                                               ABS(ALT))-.2923: GOTO 310                                                300  POSITION=-9.736999*(1.5708-ABS(ALT))-.4519:                                   GOTO 310                                                                 310  IF ALT<0 THEN POSITION=-POSITION                                         320  PRINT "THE POSITION OF THE                                                    COLLECTOR IS: ";POSITION                                                 330  END                                                                      ______________________________________                                    

It should be understood that the above equations and computer programare for a preferred embodiment in which the optimum performance issought. Other concentrators having the same general double curvatureconfiguration may be made that will work in the same way but may changethe path of movement of the zone of concentration and also reduce theability to predict the location of the zone. Therefore, the inventionshould not be construed as being limited to the exact shape or predictedmovement defined by the equations.

Referring now to FIGS. 8 through 10, a set of concentrator panels 11 isarrayed to form a structure suitable to be used as a roof-10 andincludes center uprights 30 which extend vertically from the perimeterframe 31. The panels 11 are mounted on the perimeter frame 31 and aresupported by the uprights 30 in an inclined position to maximize theefficiency of the concentrator. The collector 16 is supported by theriser supports 17 which are in turn cantilevered from the riser posts 33which are aligned at the peak of the roof structure with the uprights30. The location of the riser supports 17 are components of equation 3which determines the positioning of the collector 16. The uprights andriser post 33 are cross-braced by means of the diagonally extendingreinforcement bars 34.

It should be understood that the uprights 30, perimeter frame 31 andreinforcement bars 34 merely hold the panels in the desired orientationand are not required to maintain the curvature of the panels 11. Aspreviously mentioned, the panels are non-developable surfaces havingconsiderable structural strength thus eliminating the need for a frameto maintain their shape.

The fluid conduit 36 is shown in place on the riser support 17 and ismovable along the length of the riser support 17 to stay within theconcentration zone 13 according to equation 3 above. The collector 16includes a fluid conduit 36 which is disposed centrally within a glassinsulating tube 37 that is provided to insulate the fluid conduit 36from ambient air flow. In a preferred embodiment, the insulating tube 37maintains a partial vacuum about the fluid conduit 36. The ends of thefluid conduit are connected to a system which uses heated fluid forheating, generating electricity, or for other purposes by means of aflexible or movable connection means (not shown).

As an alternative, a photovoltaic cell could be used as the collectorfor converting the sunlight directly into electricity.

In FIG. 11 the panels 11 are shown to comprise identical sections 38,with one section extending from the crown 24 to one lateral edge 25 ofthe panel 11. By forming the panel 11 from two identical sections 38,fabrication and transportation of the panels is simplified.

Referring now to FIGS. 11 and 12, the north-south extending jointsbetween adjacent panels are shown. Upper and lower crown joint members39 and 40 are provided at the crown 24, or mid-point of the panel, topermit two sections 38 to be joined together to form the panel 11. Acrown flange 42 is provided at the north-south extending edge of eachsection 38 at the crown 24. Between lateral edges 25 of adjacent panels11, upper and lower edge joint members 43 and 44 are provided to joinadjacent panels 11 together. Upper and lower edge joint members 43 and44 engage edge flanges 46 formed on the lateral edge 25 of each panel11.

Elastomeric gasket means 45 are preferably provided on the top andbottom between surfaces of the panel 11 wherever panels are joined toprevent water from leaking between adjacent sections 38 or between apanel 11 and the frame 31. Referring to FIG. 12, elastomeric gaskets 45are shown between the panel 11 and upper and lower edge joint members 43and 44.

Other joint members are provided for joining adjacent edges of panelstogether in various combinations. For instance, in FIG. 13 a double basejoint 48 is shown wherein the end flange 49 of two panels 11 abutting attheir lower edge are secured together. Elastomeric gaskets 45 may beprovided on opposite sides of the end flange 49 to make the jointwatertight.

As shown in FIG. 14, a single base joint 50 is shown wherein a singleend flange 49 may be joined to the perimeter frame 31 with anelastomeric gasket on opposite sides of the end flange 49.

Referring now to FIG. 15, the upper and lower peak joint members 51 and52 are shown engaging two end flanges 49. Upper and lower peak jointmembers 51 and 52 are disposed at the peak of the roof 10 to attach andseal the upper end flanges 49 of adjacent panels together. As previouslydescribed, gaskets 45 are provided to seal the peak joint members 51 and52 where they engage the end flanges 49.

Referring now to FIG. 16, a portion of a drive mechanism for moving thecollector 16 along the riser support 17 is shown in detail. Theillustrated embodiment is only one of many types of drive mechanismsthat could be used to move the collector 16 and is disclosed herein asan example and not by way of limitation. The worm gear 55 is rotatablysecured to the riser support 17 and may be rotated by a reversibleelectric motor (not shown) or other rotatable drive mechanism. The wormgear 55 is engaged by a rack 53 as is well known in the gearing art. Aguide block 54 is provided on the opposite side of the riser support 17to keep the rack 53 in engagement with the worm gear 55. Preferably theelectric motor is controlled by a microprocessor (not shown) programmedwith an algorithum corresponding to equation 3 above. The collector 16is moved up and down the riser supports 17 by turning the worm gear 55to keep it in the zone of concentration 13. Alternatively, the collectorcontrol system could include a photocell control system for continuallysensing the location of the zone of concentration 13.

In the preferred embodiment, as shown in FIG. 17, each section includesan aluminum foil layer 56 having a polished side 57 which acts as thereflecting surface and a brushed side 58 that bonds to a layer of epoxy59. The epoxy 59 is in turn bonded to a molded shell 60 of fiberreinforced plastic.

The method of constructing the sections 38 to have sufficient strengthand an acceptable reflecting surface is described as follows.

Initially a panel mold is constructed which has a specially contouredsurface for molding each section 38 to have a doubly curvedconcave/convex surface. One method of forming the mold is to cut firstand second foam core pattern boards which have a convex radius on oneside corresponding to the desired curvature of the section 38 at thecrown 24 and lateral edge 25, respectively. The pattern boards are thenenclosed on their ends and bottom so that the space therebetween can befilled with plaster and reinforcing wire or mesh. A surface forming toolis provided which has a concave radius on one side corresponding to theconvex radius of curvature of the section 38 in the east-west direction.The forming tool is carefully worked over the side of the pattern boardshaving a convex radius to impart the desired shape to the contoured moldsurface.

Each section 38 is formed by first applying a release agent to the panelmold to reduce wear and permit removal of the finished panel from themold. Strips of aluminum foil 56 are then laid in the mold with thepolished surface 57 facing the mold and the brushed surface 58 facingupwardly. Care should be taken not to touch the brushed surface 58 orallow any contamination to be deposited thereon that would interferewith bonding. The aluminum foil 56 is stretched until it conformsclosely to the mold shape. The ends of the foil are then clamped inplace and an epoxy material is applied to the brushed surface 58. It isto be understood that other bonding agents may be satisfactory for thispurpose, however, epoxy has been found to provide a high quality bond.Other strips of aluminum foil 56 are laid in the mold and coated asdescribed above until the mold is completely lined with epoxy coatedaluminum foil. The adhesive is then cured for a predetermined period oftime. After curing, the epoxy coated surface of the aluminum foil issprayed or otherwise coated with fiber reinforced plastic. The fiberreinforced plastic is then cured to form the finished section 38 of apanel 11. The section 38 is trimmed to the desired dimensions andremoved from the mold ready for use.

INSTALLATION

The array of panels 11 of the present invention is installed as the roof10 of a building, by first building the perimeter frame 31 to which theuprights 30 are secured by welding or other well-known means. It ispreferred that the circular arc concentrator 10 of the present inventionbe used as the roof of the building due to the inherent strength of thepanels 11 and the ideal drainage channels formed between adjacent panels11. Center uprights 30 support the upper end flange 49 of the panels 11a predetermined height from the perimeter frame 31. The angle of thepanels 11 is determined according to the latitude of the circular arcconcentrator installation. In most cases, maximization of energycollection efficiency occurs when the panels 11 are positioned so thatthe tangent at the median point extends perpendicularly to the sun atthe vernal and autumnal equinox at mid-day. It is anticipated that insome cases maximization of energy collection in the winter or summermonths may be more important than overall maximization and that the tiltof the panels 11 may be varied accordingly.

The frame 14 may be further reinforced by means of diagonal reinforcingbars 34 extending between the uprights 30 and the perimeter frame 31.Riser posts 33 support one end of the riser support 17 in a cantileveredarrangement in conjunction with uprights 35 which extend through thepanels 11 at the crown 24 of each panel 11.

The worm gear 55 drive mechanism may be provided on one or more of theriser supports 17. The rack 53 is secured to the collector 16 forengagement with the worm gear 55 with a guide block 54 on the oppositeside of the riser support 17 from the rack 53 to guide the movement ofthe collector 16 along the riser support 17.

While the invention has been described in conjunction with a specificembodiment thereof, it is evident that many alternatives, modifications,and variations will be apparent to those skilled in the art in view ofthe foregoing description. Accordingly, it is intended to embrace allsuch alternatives, modifications, and variations that fall within thescope of the appended claims.

What is claimed is:
 1. A roof structure for a building comprising:aplurality of anticlastic panels having a light concentrating surfacebeing convex along an east-west axis and concave along a north-southaxis so that light from a distant source is focused in a narrow andsubstantially straight zone of concentration that moves in a planar pathregardless of the angle of incidence of light directed thereto; meansfor securing said panels together on adjacent edges; a frame forsupporting said panels in a stationary position on a building; acollector means for absorbing the light and converting the light intoheat and transferring the heat to a remote location, said collectormeans moving in the planar path of the zone of concentration accordingto changes in the location of the zone of concentration; and, saidconcave surface includes a crown being a generally circular arc ofradius r_(xc), first and second concave edges being concave generallycircular arcs parallel to the crown arc and having a radius r_(xe) whichis greater than r_(xc) and first and second intermediate surfacesextending between said first and second concave edges and the crownwherein said intermediate surfaces are defined by generally circulararcs varying in a monotonic increase from the crown to the first andsecond concave edges.
 2. A plurality of rigid light-concentrator panelshaving a reflective continuous anticlastic surface concave in a firstdirection having a curved arc cross-section in each plane extending inthe first direction and being convex in a second direction perpendicularto the first direction and having a curved arc cross-section in thesecond direction for providing a linear zone of concentration, saidpanels being contiguously aligned and used in a roof structure for abuilding, with the concave surface in said first direction of the panelsbeing aligned along a north-south axis and the convex surface in saidsecond direction is aligned along an east-west axis so that light from adistant source is focused in a narrow and substantially straight zone ofconcentration that moves in a planar path regardless of the angle ofincidence of light directed thereto;means for securing said panelstogether on adjacent edges; a frame for supporting said panels in astationary position on the building; a collector means for absorbing thelight and converting the light into heat and transferring the heat to aremote location, said collector means moving in the planar path of thezone of concentration according to changes in the location of the zoneof concentration; and, said concave surface of the panels having a crownbeing a substantially circular arc of radius r_(xc), first and secondconcave edges being concave substantially circular arcs parallel to thecrown arc and having a radius r_(xe) which is greater than r_(xc) andfirst and second intermediate surfaces extending between said first andsecond concave edges and the crown wherein said intermediate surfacesare defined by substantially circular arcs varying in a monotonicincrease from the crown to the first and second concave edges.